Data Free Training of Diffusion Models for Lattice Field Theories
Abstract
Sampling equilibrium field configurations remains a major computational bottleneck in lattice field theory, motivating the development of generative samplers that can produce independent configurations. Diffusion models are promising for this purpose, but their standard denoising score matching objective requires samples from the target distribution, seemingly reintroducing the original sampling problem. Here, we show that diffusion models can instead be trained from their own generated samples using the target score identity, provided access to the unnormalized probability density. Importance-weighted formulations of this identity yield a consistent target throughout training, while unweighted variants define a self-consistent fixed-point training scheme. We benchmark the different approaches in two-dimensional ϕ4 theory and identify effective choices that enable efficient training and sampling across the symmetric, critical, and broken phases. Ultimately, our data-free training approach achieves comparable performance to training on HMC reference data.
Related
- Numerical Investigations of Phase Transitions in Lattice Field Theories
- Gauge mean-field theories of the underscreened Kondo lattice
- Background Effects on Thermal Free Energy in Conformal Field Theories
- Defect conformal field theories with free-in-the-bulk fermions
- Annealed sampling of diffusion models in lattice field theory
BibTeX
@misc{grinwald2026data,
title = {{Data Free Training of Diffusion Models for Lattice Field Theories}},
author = {Dennis Grinwald and Ankur Singha and Khaled Kahouli and Karl Jansen and Shinichi Nakajima},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18863},
eprint = {2610.18863},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18863},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Data Free Training of Diffusion Models for Lattice Field Theories
AU - Dennis Grinwald
AU - Ankur Singha
AU - Khaled Kahouli
AU - Karl Jansen
AU - Shinichi Nakajima
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18863
UR - https://arxiv.org/abs/2610.18863
AB - Sampling equilibrium field configurations remains a major computational bottleneck in lattice field theory, motivating the development of generative samplers that can produce independent configurations. Diffusion models are promising for this purpose, but their standard denoising score matching objective requires samples from the target distribution, seemingly reintroducing the original sampling problem. Here, we show that diffusion models can instead be trained from their own generated samples using the target score identity, provided access to the unnormalized probability density. Importance-weighted formulations of this identity yield a consistent target throughout training, while unweighted variants define a self-consistent fixed-point training scheme. We benchmark the different approaches in two-dimensional ϕ^4 theory and identify effective choices that enable efficient training and sampling across the symmetric, critical, and broken phases. Ultimately, our data-free training approach achieves comparable performance to training on HMC reference data.
ER -